You are an economic policy analyst for Agriculture and Agrifood Canada (AAFC). You are asked to
consider the economic impact of an export quota on potash. You assume the domestic demand and supply
for potash in Canada are given by the following linear demand and supply functions:
𝑃
𝐷 = 𝛼 − 𝛽𝑞
𝑃
𝑆 = 𝑎 + 𝑏𝑞
where 𝛼, 𝛽, 𝑎, 𝑏 ≥ 0. You conduct an econometric analysis of the domestic supply and demand and
determine that the demand and supply functions are as follows:
𝑃
𝐷 = 120 − 2𝑞
𝑃
𝑆 = 2⁄5 𝑞
Canada is a potash exporter. The excess supply function for Canadian potash is the quantity difference
between supply and demand at each price, and can be calculated as follows:
𝐸𝑆 =
𝛽𝑎 + 𝛼𝑏
𝑏 + 𝛽
+ 𝑇 +
𝛽𝑏
𝑏 + 𝛽
𝑞
where 𝑇 is the transportation cost. You also assume a linear excess demand function, 𝐸𝐷 = 𝐴 − 𝐵𝑞, with
the elasticity of 𝐸𝐷 given by:
𝜀𝐸𝐷 =
𝑑𝑞
𝑑𝑝
𝑝𝑊
𝑞
=
−1
𝐵
𝑝𝑊
𝑞
, so that 𝐵 =
−1
𝜀𝐸𝐷
𝑝𝑊
𝑞
and 𝐴 = 𝑝
𝑊 (1 −
1
𝜀𝐸𝐷
).
You determine that the elasticity of 𝐸𝐷 is equal to −
2
3
, the world price is $60/unit, and the transportation
cost is $10/unit. As an economist at AAFC, you are asked to:
(a) Determine the effect of international trade in potash on the Canadian economy. In particular, you
are asked to calculate the net gain to Canada due to trade (compared to autarky). You are also
asked to calculate the impact of potash trade on Canadian consumers and producers of potash.
a. What are the formulae for the equations of 𝐸𝐷 and 𝐸𝑆?
b. Draw a diagram with a panel for the domestic market and a panel for the international
trade market. Plot the domestic supply and demand curves in the domestic panel, and the
excess supply and excess demand curves in the international trade panel. Show the gains
and losses from trade in each of the panels and provide an actual measure of the net gain
to trade. Show the gains/losses to Canadian consumers and producers in the domestic
panel.
(b) Now suppose that Canada sets an export quota of 36 units of potash.
a. What are the total gains or losses (compared to autarky)?
b. Is Canada better off with an export quota or with free trade?
(c) In reality, Canada has formed an export cartel in potash (two Canadian companies and one US
company) in an effort to exploit market power on the world market. In theory, how should you
amend your analysis to take this into account?